Optimality Conditions for Bilevel Imaging Learning Problems with Total Variation Regularization
| Autor: | Reyes, Juan Carlos De los, Villacís, David |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | We address the problem of optimal scale-dependent parameter learning in total variation image denoising. Such problems are formulated as bilevel optimization instances with total variation denoising problems as lower-level constraints. For the bilevel problem, we are able to derive M-stationarity conditions, after characterizing the corresponding Mordukhovich generalized normal cone and verifying suitable constraint qualification conditions. We also derive B-stationarity conditions, after investigating the Lipschitz continuity and directional differentiability of the lower-level solution operator. A characterization of the Bouligand subdifferential of the solution mapping, by means of a properly defined linear system, is provided as well. Based on this characterization, we propose a two-phase non-smooth trust-region algorithm for the numerical solution of the bilevel problem and test it computationally for two particular experimental settings. Comment: 33 pages, 9 figures, 4 tables |
| Databáze: | arXiv |
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